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Cellularization of structures in stable homotopy categories

Published online by Cambridge University Press:  17 May 2012

JAVIER J. GUTIÉRREZ
JAVIER J. GUTIÉRREZ*
Affiliation:
Departament d'Àlgebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain. e-mail: javier.gutierrez.math@gmail.com
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Abstract

We describe the formal framework for cellularization functors in triangulated categories and study the preservation of ring and module structures under these functors in stable homotopy categories in the sense of Hovey, Palmieri and Strickland, such as the homotopy category of spectra or the derived category of a commutative ring. We prove that cellularization functors preserve modules over connective rings but they do not preserve rings in general (even if the ring is connective or the cellularization functor is triangulated). As an application of these results, we describe the cellularizations of Eilenberg–Mac Lane spectra and compute all acyclizations in the sense of Bousfield of the integral Eilenberg–Mac Lane spectrum.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 153 , Issue 3 , November 2012 , pp. 399 - 418
Copyright
Copyright © Cambridge Philosophical Society 2012

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